Aperiodic transformer



Aug. 22, 1939. ALFQRD I 2,170,626

APERIODI C TRANSFORMER Filed Dec. 28, 1937 3 Sheets-Sheet 1 INVENTORANDREW ALfO/FD BY a 3 ATTORNEY Aug. 22, 1939.

APER IODI C TRANSFORMER A. ALFORD Filed Dec. 28, 1937 FIGS.

3 Sheets-Sheet 2 %s2 130 104 1so ATTO RN EY INVENTOR Aug. 22, 1939. A.ALFQRD 2,170,626

APERIODIC TRANSFORMER v Filed Dec. 28, 193'? 3 Sheets-Sheet 3 F'l-GJO.

3.0 a f m 2-0 V r zlm INVENTOR ATTO F: N EY Patented Aug. 22, 1939UNITED STATES PATENT OFFIQE APERIODIG TRANSFORMER Application December28, 1937, Serial No. 182,092

6 Claims.

The present invention relates to high frequency transformers andespecially to that type of transformer which consists essentially of atransmission line having variable characteristics along its length.

It is an object of my invention to provide a high frequency aperiodictransformer which shall be of convenient dimensions and of unusuallysimple construction. Particularly it is an object to provide atransformer of simple construction which is capable of transforming,without substantial reflection, waves whose wavelength is more thantwice as long as the overall length of the transformer itself, even whenthe transformation ratio is as great as 1.2 to 1.

Another object of my invention is to provide such a transformer which isadapted to be constructed with the same materials and according to thesame general principles of construction as are employed in erectingordinary open-wire transmission lines. In accordance with my invention,an aperiodic transformer of conveniently small dimensions may beconstructed with the same materials as are ordinarily employed inerecting open-wire transmission lines, and the construction may beperformed by the same construction gangs who are employed for erectingantennae and transmission lines in the field and who are primarilyskilled in the art of antenna and line construction.

One particularly useful feature of my invention is the arrangementwhereby a desired curve of wire spacing may be very simply attained bythe determination of only a very few dimensions, the construction beingsuch that all the other spacing dimensions inherently assume the correctvalues when these very few dimensions are properly determined. Inaccordance with my invention, a transformer can readily be erected whosespacing distances are so accurately determined at all points that thetransformer can, with substantially no reflection, transmit waves whosewavelength is four or more times the total length of the transformer,even when the transformer wire spacing at the high impedance end isseveral times as great as at the low impedance end.

Transformers of the tapered transmission line type have previously beensuggested, in which discontinuously loaded telephone lines wereproportioned by varying the magnitude or spacing of the loading coils soas to obtain a desired result. Such transformers, however, have not beenwell adapted for use with high frequencies nor with unloaded, open-wirelines. High frequency transformers have also been suggested in which theline spacings of an open-wire transmission line were varied along thelength of the line, but the spacings of these transformers have beenvaried either in accordance with a straight taper or in accordance withsome other incorrect curve, so that these transformers have not beencapable of usefully transforming, with substantially no reflection,waves Whose wavelength was three or more times the length of thetransformer itself.

In accordance with the present invention, a high frequency aperiodictransformer is constructed in the form of an open-wire transmission linewithout loading coils, so that the velocity of propagation of wavesalong this transformer remains substantially constant and substantiallyequal to the speed of light, and the surge impedance of this transformeris varied from point to point along the length of the transformer bymerely varying the spacing between the two wires of the transformer inaccording with the formula where s is the center-to-center spacing ofthe two wires at any plane of measurement; 1' is the radius of each ofthe wires; P is the distance of the plane of measurement from the lowimpedance end of the transformer, expressed as a fraction of the totaltransformer length; e is the base of natural logarithms; M and N areparameters determined by the terminal spacings at the ends of thetransformer.

By constructing a transformer in this manner it is unnecessary to varythe shape or size of the wires composing the transformer, and it is alsounnecessary to connect inductances or capacitances in series or shuntwith the line wire. The only dimension which must be varied along thelength of the transformer is the spacing between the two wires whichconstitute the conductors of the transformer. It has been foundexperimentally that a transformer whose spacing varies in accordancewith Formula (1) above set forth and whose wire diameter is constant iscapable of transmitting, between lines whose surge impedances have aratio of 14:10 or 13:10, and with substantially no reflection, waveswhose wavelength varies between the shortest length available formeasurement and a length which is three or four times as great as theoverall length of the transformer itself.

In order to space the transformer conductors in accordance with Formula(1) it is possible to employ a large number of spreaders whose lengthsand positions along the transformer are computed in accordance with theformula. In accordance with a further feature of the present invention,however, the spacing between conductors may be made to vary according toa curve closely approximating the curve defined by Formula (1) merely bystretching the two conductors as straight lines between a pair of lowimpedance terminals spaced apart a distance d and a pair of highimpedance terminals spaced apart a distance D. In order that such anarrangement may produce a curve of wire spacing which approximates thedesired curve, the axis of the low impedance terminals should not lie inthe same plane as the axis of the high impedance terminals, but shouldbe inclined at an angle s with respect thereto. Assuming that the axisof the high impedance terminals is inclined at the angle with respect tothe axis of the low impedance terminals, and that the distance betweenthe high impedance terminals is D and the distance between the lowimpedance terminals is d, the spacing s between the two wires in anygiven plane of measurement perpendicular to the axis of the transformeris given by the following general formula:

where P is the distance of the plane of measurement from the lowimpedance end of the transformer, expressed as a fraction of the totallength of the transformer. When the angle is taken to be the aboveFormula 2 may be expressed as follows:

Because of the greater convenience of running all transmission lineseither in a horizontal or a vertical plane, it will be assumed that thehigh impedance and low impedance terminals of the transformer are alwaysat right angles, so that Formula (3) may be used instead of Formula (2)in all those cases where the transformer conducto'rs are stretched asstraight lines between the high impedance and low impedance terminals.

The preferred construction of the present invention may best beunderstood by reference to the accompanying drawings, in which Fig. 1 isa perspective view of the simplest form of transformer in accordancewith my invention, connected between a transmission line which extendsfrom a receiving antenna and a building which houses a receivingequipment;

Fig. 2 is a side elevation of the transformer shown in Fig. 1;

Fig. 3 is a plan projection of the transformer shown in Fig. 2 as viewedin the direction of the arrows 3, 3 of Fig. 2;

Fig. 4 is an end elevation of the transformer shown in Fig. 2 as viewedin the direction of the arrows 4, 4 of Fig. 2;

Fig. 5 is a side elevation of a preferred form of transformer inaccordance with my invention;

Fig. 6 in a plan projection of the transformer shown in Fig. 5 as viewedin the direction of the arrows 6, 6 of Fig. 5;

Fig. '7 is an end elevation of the transformer shown in Fig. 5 as viewedin the direction of the arrows 1, l of Fig. 5;

Fig. 8 is an enlarged schematic representation of the conductor portionsof the transformer shown in. Fig. '7;

Fig. 9 is an inclined projection of the transformer shown in Fig. 7 asviewed in the direction of the arrows 9, 9, of Fig. 7;

Fig. 10 is a graphical representation of the spacing between conductorsat different points along the length of two transformers of differentdimensions; constructed according to Figs.

Referring now more particularly to Fig. 1, I0! is a building inwhich ishoused a radio receiving equipment (not shown). Through the wall of thisbuilding extend two lead-in insulators Hi3 and I 94. A cross arm H15mounted on a pole (not shown) carries two petticoat insulators Hi5 andIN. Stretched between the leadin insulators H13 and use and thepetticoat insulators m5 and H)? are the two transformer conductors H20and i353 which essentially constitute the transformer of my invention.The petticoat insulators I96 and i8? are disposed horizontally andspaced so that at the end points l2! and 139 the conductors I29 and 139are spaced twelve inches apart center-to-center. The leadin insulatorsI03 and it, on the other hand, are vertically disposed and spaced sothat at the end points I 22 and I33 conductors I20 and I30 are spacedfour inches apart center-to-center. Because of the angular relationbetween the end points l2l-l3l and the end points IZZ-ISZ, the spacingbetween conductors I20 and I30 does not vary linearly from one end ofthe transformer to the other, but varies in accordance with the curvedefined by Equation (3) set forth above. This curve of spacing will havethe general form of the curves shown in Fig. 10, which represent thespacings for transformers of similar construction in which the highimpedance. spacings are respectively six and two times the low impedancespacing instead of being three times the low impedance spacing as in thetransformer of Fig. 1.

Although the curve of variation of conductor spacing of the transformershown in Fig. 1, as well as of the other two transformers represented bythe curve of Fig. 10, is not theoretically identical with the curve ofconductor spacing defined by Formula (1) set forth above, it has beenfound empirically that these curves approximately agree. More precisely,it has been found that the curve of conductor spacing of a transformersuch as represented in Figs. 1 and 10,. agrees with the curve ofconductor spacing which would be obtained if two transformers, eachdesigned in accordance with Formula (1), were connected endto-end, oneof these two transformers being a step-down transformer and the otherone a stepup transformer of smaller ratio. Thus a transformer designedas shown in Fig. 1, or as represented in either of the curves of Fig.10, is capable of transforming without appreciable reflection waveswhose wavelength is several times the overall length of the transformeritself.

Experimental tests have also confirmed the fact that a transformerdesigned in accordance with Fig. 1 or Fig. 10, provides anefficient,substantially reflection-free arrangement for steppingup orstepping-down voltage, or current, or impedance over a frequency rangewhose upper limit is practically unlimited and whose lower limitcorresponds to a wavelength between two and four times the length of thetransformer itself for transformation ratios of the approximate orderrequired in practice.

Figs. 2, 3 and 4 represent orthographic projections from differentdirections of the transformer shown in Fig. 1. As can be seen mostclearly from Fig. 3, the vertical disposition of the transformerconductors at the point where they enter the receiver building permitsthe transformer to be.

brought up to the building at any convenient angle, without introducingan objectionable difference in length in the two line conductors. Forthis reason it is ordinarily preferred to arrange the terminals I22 andI32 in a vertical plane as shown, and to arrange the terminals iii andIt! in a horizontal plane. Furthermore, the arrangement of terminals I28and it! in a horizontal plane is particularly convenient when thetransmission line to which the transformer is connected, is supported inthe ordinary way upon horizontal cross arms which carry a plurality ofpetticoat insulators, such as I06 and I01.

Referring now more particularly to Figs. 5, 6, '7, 8 and 9, thesefigures represent a preferred form of transformer in accordance with myinvention. This form of transformer is almost as simple to construct asthe form illustrated in Figs. 1, 2, 3 and 4, and has the advantage thatthe curve of conductor spacing along the length of the transformer iseven more closely like the ideal curve defined in Formula (1) than thespacing curve of the simpler form of transformer. As shown in Figs. 5,6, '7, 8 and 9, this preferred form of transformer is essentiallysimilar to the form illustrated in Figs. 1-4, but further comprises oneintermediate insulating spacer I50 located intermediate the ends of thetransformer, at a distance A from the low impedance end and at adistance B from the high impedance end of the transformer. Thisinsulating spacer I50 serves as a spreader to keep the wires apart andis of length E which is less than length D but greater than length d.The length E of the spreader I52 is greater than the spacing betweenconductors I20 and I30 would be if the spreader were not provided. Thedistance A of the spreader from the low impedance end of the transformeris of the order of one-third of the total transformer length, thisdistance A being ordinarily between one-sixth and one-half of the totaltransformer length. The length E of the spreader is preferablysubstantially equal to the ideal conductor spacing at a plane A unitsfrom the low impedance end of the transformer, as determined from thetheoretical Formula (1) set forth above.

In computing the conductor spacing at various points along the length ofa transformer such as shown in Figs. 5, 6, 7 8 and 9, the transformermay be considered as two simple transformers of the type illustrated inFig. 1, these two transformers being connected together end-to-end. Ofthese two transformers the low impedance one may be considered as havinga length A, a low impedance terminal spacing d, and a high impedanceterminal spacing E. The higher impedance one of the two transformers maybe considered as having a length B, a low impedance terminal spacing E,and a high impedance terminal spacing D. Although the overall anglebetween the axes of terminals IZI and HI and terminals I22 and I32 isstill 90 in this form of transformer, the individual angles of the twocomponent transformers will no longer be 90. For the low impedance oneof the two component transformers, the angle may be considered to beequal to 0 as shown in Fig. 8; while for the high impedance one of thetwo component transformers, the angle may be considered to be 900. Theangle 0 will depend upon the distances A and B which define the positionof the spreader I50. The angle 6 may be computed from the followingformula:

0' cos 6 D sin 0 This formula will be understood by inspection of Figs.9 and '7 or 9 and 8, Fig. 8 being merely an enlarged representation ofthe conductor portions of Fig. 7 with the supporting structure removedand with dimensions added. The above Formula (4) is derived upon theassumption that the fundamental angle between the terminals HI and I3Iand the terminals I22 and I32 is 90 for the complete transformer. It isclear that if this angle were different from 90 the expression sin 0 inFormula (4) would have to be replaced by the expression cos (6).

Although it is preferred that the spreader I50 should be located roughlyone-third of the way from the low impedance end towards the highimpedance end of the transformer as previously explained, the locationof this spreader is not critical. If the spacing ratio D/d of thetransformer is as great as 6, the spreader I50 may be located as near tothis low impedance end of the transformer as one-seventh of the totaltransformer length and still the transformer will give good results. Ifthe transformer spacing ratio is as low as 2, on the other hand, thespreader I50 may be located as much as two-thirds of the transformerlength from the low impedance end of the transformer. Thus the abovementioned rule that the spreader should be located at a distance fromthe low impedance end which is of the order of one-third of the totaltransformer length, can only be considered as an approximate ruleapplicable to transformers which have spacing ratios of the magnitudemost commonly used.

For any given transformer spacing ratio the optimum position for thespreader I50 can be approximately determined from an inspection of thespacing curve of the transformer conductors without a spreader.Referring to Fig. 10, for example, which graphically represents thevariation of conductor spacing along the transformer length for atransformer having a spacing ratio of 6 and for another transformerhaving a spacing ratio of 2, it will be observed that for thetransformer with a spacing ratio of the conductor distance becomes lessthan (1 at a point which is .4 times the transformer length from the lowimpedance terminal. Therefore, if the ideal desired curve of conductorspacing must not at any point become less than the low impedancedistance d, it is clear that the spreader should be set more than .4times the transformer length from the low impedance terminals in thecase of a transformer having a spacing ratio of 2. For such atransformer, a satisfactory value of A would be approximately .5 to .8times the total transformer length. On the other hand, for a transformerwhose spacing ratio D/d was equal to 6, a much smaller value of A wouldclearly be suitable. As can be seen from the upper curve of Fig. 10, theconductor separation for such a transformer does not fall below thevalue d until the plane of measurement is about .07 times the totaltransformer length from the low impedance terminal. For such atransformer, therefore, the distance A could be taken to be somewherebetween .2 and .6 times the total transformer length. If a very accuratetransformer design is desired, the optimum position of the spreader $50can be still more accurately determined by first estimating the regionfor locating this spreader from curves such as shown in Fig. 10 in themanner above outlined, and then assuming two different spreaderlocations within this estimated region. The resulting curves ofconductor spacing for the two assumed positions of the spreader may thenbe readily calculated from Formulae (2) and (4), and these two curvescan then be compared with an ideal curve plotted from Formula (1).Ordinarily both of the assumed curves will be sufficiently closelysimilar to the ideal curve for all practical purposes, but by checkingone or two assumed curves in the manner just outlined, it is possible toobtain a still more accurate correspondence between the actual conductorspacing and the ideal conductor spacing.

It is, of course, apparent that more than one spreader might be employedin order to obtain a still more accurate correspondence between theactual and theoretical conductor spacing, although it is believed thatin practice a single spacer is sufficient when the transformer is con--structed in accordance with Figs. 5, 6, 7, 8 and 9. In any event thenumber of spacers required for simulating: the theoretically desiredcurve with a given degree of approximation will always be considerabiylessened by the twisting arrangement of the present invention.

While certain embodiments of my invention have been disclosed for thepurpose of illustration, it will be understood that modifications,adaptations and variations thereof such as would occur to one skilled inthe art may be made without departing from the scope of my invention asdefined in the appended claims.

What I claim is:

1. A high frequency aperiodic transformer comprising a first pair ofsupports, a second pair of supports spaced from said first pair ofsupports and disposed in a different plane from that of said first pairand separated by a smaller distance than said first pair of supports,and two conductors of substantially uniform cross-section each stretchedfrom one of said first pair of supports to one of said second pair ofsupports said supports being so related that said conductors are not inthe same plane, whereby a non-linear spacing relationship exists betweenthe conductors to effect the desired impedance transformation.

2. A high frequency aperiodic transformer comprising a first pair ofsupports, a second pair of supports disposed in a different planearranged at an angie to the plane of said first pair and separated by asmaller distance than said first pair of supports, and two conductors ofsubstantially uniform cross-section each extending substantiallylinearly from one of said first pair of supports to one of said secondpair of supports said conductors being in mutually exclusive planes,whereby a non-linear spacing relationship exists between saidconductors.

3. A transformer arrangement in accordance with claim 2, wherein saidtwo conductors are extended to a third pair of supports which lie in adifferent plane from that of said second pair of supports arranged at anangle to said first named different plane and separated by a stillsmaller distance than said second pair of supports, and conductorsbetween said second and third supports arranged in mutually exclusiveplanes to form an additional transformer.

4. A high frequency aperiodic transformer comprising a first pair ofsupports lying in a first line, a second pair of supports spaced fromsaid first pair of supports and lying in a second line which forms anangle with said first line, a first conductor stretched between onesupport of said first pair and one support of said second pair, a secondconductor stretched between the other support of said first pair and theother support of said second pair, and a spacer fixing the mutualseparation of said conductors intermediate said supports whereby saidtwo conductors form two component transformers each consistingessentially of two straight conductors and joined end to end theconductors of each transformer lying in mutually exclusive planeswhereby linear spacing relationship exists therebetween.

5. A transformer according to claim 4, wherein said angle is 90.

6. A high frequency aperiodic transformer comprising a first pair ofsupports lying in a first line, a second pair of supports lying in asecond line which forms an angle of 90 with said first line, a firstconductor stretched between one support of said first pair and onesupport of said second pair, and a second conductor stretched betweenthe other support of said first pair and the other support of saidsecond pair whereby a non-linear spaced relationship exists between saidconductors and the desired impedance transformation action is produced.

ANDREW ALFORD.

